tan-1 y y² +1 tan-1 y ) dy

Q: y = (sin x)e¯* find de sin-1y %3D d In x

A: y=sinxe-x. Then we have to find desin-1ydlnx.

Q: y sin(Vu +3u-1) Oy = Vx x+ vZx y = e* sec(tan(x*)) y%3D u = In cos(x? + 1)|

A:

Q: sec" y dy- (f) tan y

A: Topic = Integration

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: 2) dx Ve -1 a) 2 vezr - 1 In (e – 1), c) arctan (e), d) sec-le

A: We need to solve the integral

Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

Q: 1. S sin’y (2 – 3 cos y)°dy

A:

Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

A:

Q: Solve y y (x, 0) = 3 sin 2n x, y (0, t) = 0 =y (1, t); 0 0. %3D

A:

Q: sin (y) x° dy – x tan(y) dy

A:

Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: tan 0 d 30. dO sec² y dy

A:

Q: 3 - y cos xy - 4x ) dx + (- 2x+3y x cos xy + 2y) dy = 0 - | 2x+3y 2.

A: Compare the given equation with Mdx+Ndy=0 to obtain M and N. Calculate the partial derivatives of M…

Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

A:

Q: x cos'(y)dx + tan y dy = 0, y(4) = 7 2. X COS

A:

Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

A:

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

A:

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: sin y(x + sin y) dx + 2x² cos y dy = 0.

A: Given equation is  siny(x+siny)dx+2x2cosydy=0

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

A:

Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: 3 x* cos(3 y) 2 x³ sin(3 y) dx + + 2 x2 ) dy = 0

A:

Q: (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy-5yzª dz

A: Find the value of function using integrate Compare the given expression with Mdx+Ndy+Pdz to obtain…

Q: Solve ởy ôt y (x, 0)= 3 sin 2n x, y (0, t) = 0 = y (1, t); 0 0. %3D ốt

A:

Q: xy" - y' + 4x y= 0, x> 0; y,(x) = = sin x

A:

Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

Q: 2-+x* cos y = 0 dy y

A:

Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: 2. sin y(x + sin y)dx + 2x² cos ydy = 0

A:

Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: i. y = x-% % -4Vx ii. y = x+Inx+ sin(3x) iii. y = x° cOS X y = x° cos x

A: Use product rule of differentiation

Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: [x 2. x tan --yjA +xdh = 0; when x=0, y=z/2 ......

A: Given differential eqution  x tan2yx-y dx +xdy=0      ;  y0=π2

Q: 25) y" + y = 2 cos(t), y(0) = 2, y'(0) = 0.

A: Use second order differential equation

Q: cos(0)x – sin(0)y] sin(0)x + cos(0)Y T z || నా

A:

Q: Obtain the solution (3tan x-2cos y) sec^2x dx + tan x sin y dy = 0

A:

Q: b) x siny-ycos x- y = 1.

A:

Q: dy ху* - сosx sin x . У (0) -2 y(1–x²) dx

A:

Q: 3. sin x cos y dx + cos x sin y dy

A:

Q: b- y" -y+2y+ cos x, 05x y(0) -0.3, y()--0.1

A: To show the boundary value problem has unique solution we solve the given ode by method of…

Q: +7 -3y = 20 sin (x), y(0) = - 1, y(0) = 2, dy.3y %3D Q5 5 dx dx

A:

Q: 1) S 2 sec y (tany – sec y) dy

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Hei! If y cos(xy) dydx = x=0 y=0

A:

Q: Obtain a family of solution 1. [x-y arctan(y/x)]dx + x arctan (y/x)dy = 0

A: Solution is given below:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.